6. MATTER-ENERGY CONTENT OF THE UNIVERSE

In early papers on dark matter the total density due to visible and dark
matter was estimated to be about 0.2 of the critical cosmological
density. These estimates were based on the dynamics of galaxies in
groups and clusters. This density estimate can be interpreted in two
different ways: either we live in an open Universe where the total
density is less than the critical density, or there exists some
additional form of matter/energy which allows the Universe to be closed,
i.e. to have the critical total density. The additional term was
identified with the Einstein
-term, so that the
total matter/energy density was taken to be equal to the critical
cosmological density
(Gunn &
Tinsley 1975,
Turner et
al. 1984,
Kofman &
Starobinskii 1985).
Initially there was no direct observational evidence in
favour of this solution and it was supported basically on general
theoretical grounds. In its early evolution the size of the Universe
increases very rapidly and any deviation from the exact critical density
would lead to a rapid change of the relative density, either to zero, if
the initial density was a bit less than the critical one, or to
infinity, if it was greater than critical. In other words, some fine
tuning is needed to keep the density at all times equal to the critical
one.

In subsequent years several new independent methods were applied to
estimate the cosmological parameters. Of these new methods two desire
special attention. One of them is based on the measurements of small
fluctuations of the Cosmic Microwave Background (CMB) radiation, and the
other on the observation of distant supernovae.

According to the present cosmological paradigm the Universe was
initially very hot and ionized. The photons provided high pressure and
prevented baryons from moving. Perturbations of baryons did not grow,
but oscillated as sound waves. The largest possible wavelength of these
oscillations is given by the sound horizon size at the decoupling. This
wavelength is seen as the first maximum in the angular power spectrum of
the CMB radiation. The following maxima correspond to overtones of the
first one. The fluctuations of CMB radiation were first detected by the
COBE satellite. The first CMB data were not very accurate, since
fluctuations are very small, of the order of 10-5. Subsequent
experiments carried out using balloons, ground based instruments, and
more recently the Wilkinson Microwave Anisotropy Probe (WMAP) satellite,
allowed to measure the CMB radiation and its power spectrum with a much
higher precision
(Spergel et
al. 2003).
The position of the first maximum of the power
spectrum depends on the total matter/energy density. Observations
confirm the theoretically favoured value 1 in units of the critical
cosmological density, see Fig. 15.

Figure 15. Upper panel shows the acoustic
peaks in the angular power spectrum of
the CMB radiation according to the WMAP and other recent data, compared
with the CDM
model using all available data. The lower panel
shows the signature of baryonic acoustic oscillations in the matter
two-point correlation function
(Eisenstein
et al. 2005,
Kolb 2007)
(reproduced by permission of the author).

When recombination begins, the small overdensities of baryon gas launch
spherical shock waves in the photon-baryon fluid. After some time
photons completely decouple from baryons, and the baryons loose photon
pressure support. The shock stops after traveling a distance of about
150 Mpc (in comoving coordinates). This leads to an overdensity of the
baryonic medium on a distance scale of 150 Mpc. This overdensity has
been recently detected in the correlation function of Luminous Red Giant
galaxies of the SDSS survey
(Eisenstein
et al. 2005,
Hütsi
2006),
see lower panel of Fig. 15. Baryonic
acoustic oscillations depend on both the total matter/energy density and
the baryon density, thus allowing to estimate these parameters.

Another independent source of information on cosmological parameters
comes from the distant supernova experiments. Two teams, led by Riess et al.
(1998,
2007)
(High-Z Supernova Search Team) and
Perlmutter
et al. (1999)
(Supernova Cosmology Project), initiated programs to
detect distant type Ia supernovae in the early stage of their evolution,
and to investigate with large telescopes their properties. These
supernovae have an almost constant intrinsic brightness (depending
slightly on their evolution). By comparing the luminosities and
redshifts of nearby and distant supernovae it is possible to calculate
how fast the Universe was expanding at different times. The supernova
observations give strong support to the cosmological model with the
term, see
Fig. 16.

Figure 16. Results of the Supernova Legacy
Survey: apparent magnitudes of
supernovae are normalised to the standard
CDM model, shown as
solid line. Dashed line shows the Einstein-de Sitter model with
m = 1
(Kolb 2007)
(reproduced by permission of the author).

Different types of dark energy affect the rate at which the Universe
expands, depending on their effective equation of state. The
cosmological constant has one equation of state. The other possible
candidate of dark energy is quintessence (a scalar field) that has a
different equation of state. Each variant of dark energy has its own
equation of state that produces a signature in the Hubble diagram of
the type Ia supernovae
(Turner 2003).

The combination of the CMB and supernova data allows to estimate
independently the matter density and the density due to dark energy,
shown in Fig. 17. The results of this combined
approach imply that the Universe is expanding at an accelerating rate. The
acceleration is due to the existence of some previously unknown dark
energy (or cosmological constant) which acts as a repulsive force (for
reviews see
Bahcall et
al. 1999,
Frieman et
al. 2008).

Independently, the matter density parameter has been determined from
clustering of galaxies in the 2-degree Field Redshift Survey and the
Sloan Digital Sky Survey. The most accurate estimates of cosmological
parameters are obtained using a combined analysis of the 2dFGRS, SDSS
and the WMAP data
(Spergel et
al. 2003,
Tegmark et
al. 2004,
Sánchez et
al. 2006).
According to these studies the matter density parameter is
m = 0.27
± 0.02, not far from the value
m = 0.3,
suggested by
Ostriker &
Steinhardt (1995)
as a concordant model. The combined method yields for the
Hubble constant a value h = 0.71 ± 0.02 independent of other
direct methods. From the same dataset authors get for the density of
baryonic matter,
b = 0.041
± 0.002. Comparing
both density estimates we get for the dark matter density
DM =
m -
b = 0.23,
and the dark energy density
=
0.73. These parameters imply that the age of
the Universe is 13.7 ± 0.2 Gigayears.

Studies of the Hubble flow in nearby space, using observations of type
Ia supernovae with the Hubble Space Telescope (HST), were carried out by
several groups. The major goal of the study was to determine the value
of the Hubble constant. As a by-product also the smoothness of the
Hubble flow was investigated. In this project supernovae were found up
to the redshift (expansion speed)
20000 km s-1. This project
(Sandage et
al. 2006)
confirmed earlier results that the Hubble flow is very
quiet over a range of scales from our Local Supercluster to the most
distant objects observed. This smoothness in spite of the inhomogeneous
local mass distribution requires a special agent. Vacuum energy as the
solution has been proposed by several authors
(Baryshev et
al. 2001
and others). Sandage emphasises that no viable
alternative to vacuum energy is known at present, thus the quietness of
the Hubble flow gives strong support for the existence of vacuum energy.